## CHAINS, not required. Good puzzles.

Post puzzles for others to solve here.
if i was on something then:

want to see the same move again else where on that same puzzle?

i don't know why it works but it does.

i still can't prove it neither, so i wrote a page on how to identify and use them. {proff remains buried in massive subnet-forcing chains} which i can't find yet.

closest thing to an explination has something to due with a theory ive been working on for np=n question.

using certificates to reduce/remove issometric solutions by restrictions of information that has greates divergence from the other item in quarry, then identifies issometrics as the same befor calculating.

http://forum.enjoysudoku.com/viewtopic.php?t=5192

a nonfun read if you can make any sence out of that jumbled mess. it is a math of limits, using constraints of a row to form a "certificate" that creates a single solution by restricing the variable with degree of greatest diversity. basically in this case it takes the 7 and restics its placement with the chain of pairs, and all possible solutions of a row are reduced down to issometric solutions = all the same solution.

Code: Select all
`*-----------------------------------------------------------*  | 2-7    269   8     | 1247  2367  346   | 5     1239  23    |  | 1     3     79    | 8     27    5     | 249   6     24    |  | 4     26    5     | 12    9     36    | 8     123   7     |  |-------------------+-------------------+-------------------|  | 9     4     23    | 6     5     1     | 237   27    8     |  | 8     7     23    | 49   23    49    | 6     5     1     |  | 6     5     1     | 27    8     37    | 234   234   9     |  |-------------------+-------------------+-------------------|  | 37#    8     679   | 5     1     2     | 3479  347   46    |  | 235#   1     67    | 79    4     679   | 23    8     235   |  | 257#   29    4     | 3     67    8     | 1     279   256   |  *-----------------------------------------------------------* `

yield chain type 2
conjugated als (35+n) where n = 7
r7c1 {37}
r8c1 (35)
R9c1 (57)

implyes 7 cannot fall outside the row.meaning
r1c1 cannot = 7
Last edited by StrmCkr on Sat Mar 03, 2007 3:05 pm, edited 1 time in total.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1170
Joined: 05 September 2006

StrmCkr wrote:i don't know why it works but it does. i still can't prove it neither.

I think you are conveniently ignoring the cases when it doesn't work.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

show me where it doesn't work,

find an example using my method then post where it fails.

i still haven't found one.

heres another diffrent puzzle where it works again.

Code: Select all
` *-----------* |6..|.2.|..8| |...|6.1|...| |2.1|...|6.4| |---+---+---| |.9.|...|.8.| |1..|7.8|..6| |...|1.9|...| |---+---+---| |3..|5.7|..2| |9.6|.8.|5.1| |.5.|...|.4.| *-----------*after ss.  *-----------------------------------------------------------------------------* | 6       37-4     34579@   | 349@     2       345@     | 37      1       8       | | 457     8       34579   | 6       3457    1       | 237     2357    3579    | | 2       37      1       | 8       3579    35      | 6       3579    4       | |-------------------------+-------------------------+-------------------------| | 457     9       3457    | 234     6       2345    | 1       8       357     | | 1       234     2345    | 7       345     8       | 2349    2359    6       | | 4578    6       234578  | 1       345     9       | 2347    2357    357     | |-------------------------+-------------------------+-------------------------| | 3       1       48      | 5       49      7       | 89      6       2       | | 9       247     6       | 234     8       234     | 5       37      1       | | 78      5       278     | 239     1       6       | 378     4       379     | *-----------------------------------------------------------------------------*`

yielding chain type 1:
conjugated als (59+4)
R1c3 (459)
R1c4(49)
R1c6(459)

removes 4 from
r1c2.

and the puzzle solves as singles.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1170
Joined: 05 September 2006

I like the pattern, it is quite a tough nut to crack!

Code: Select all
`6 . .|. 1 .|. . 9. . 5|. . .|4 . .. 9 8|3 . .|. 6 .-----+-----+-----. . 1|. 7 4|. . .9 . .|6 . 1|. . 4. . .|8 9 .|3 . .-----+-----+-----. 8 .|. . 3|9 4 .. . 2|. . .|8 . .3 . .|. 8 .|. . 6`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

wapati wrote:I like the pattern, it is quite a tough nut to crack!

Code: Select all
`6 . .|. 1 .|. . 9. . 5|. . .|4 . .. 9 8|3 . .|. 6 .-----+-----+-----. . 1|. 7 4|. . .9 . .|6 . 1|. . 4. . .|8 9 .|3 . .-----+-----+-----. 8 .|. . 3|9 4 .. . 2|. . .|8 . .3 . .|. 8 .|. . 6`

Well, the initial eliminations are interesting.

Code: Select all
`# SSTS: Singles, Naked Pair, Naked Triple, Locked Candidate (1)#         X-Wing    r19 /c24  => [r8c24]<>4# Sashimi X-Wing    r14 /c49  => [r3c9 ]<>5# finned  X-Wing    c67 /r39  => [r3c9 ]<>7# finned  X-Wing    r47 /c49  => [r9c4 ]<>2# finned  Swordfish c459/r347 => [r3c6 ]<>2# SSTS:   Multiple Colors     => [r1c2 ]<>2# SSTS:   Multiple Colors     => [r3c9 ]<>2`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

StrmCkr wrote:show me where it doesn't work,

find an example using my method then post where it fails.

i still haven't found one.

heres another diffrent puzzle where it works again.

Code: Select all
` *-----------* |6..|.2.|..8| |...|6.1|...| |2.1|...|6.4| |---+---+---| |.9.|...|.8.| |1..|7.8|..6| |...|1.9|...| |---+---+---| |3..|5.7|..2| |9.6|.8.|5.1| |.5.|...|.4.| *-----------*after ss.  *-----------------------------------------------------------------------------* | 6       37-4    34579@  | 349@    2       345@    | 37      1       8       | | 457     8       34579   | 6       3457    1       | 237     2357    3579    | | 2       37      1       | 8       3579    35      | 6       3579    4       | |-------------------------+-------------------------+-------------------------| | 457     9       3457    | 234     6       2345    | 1       8       357     | | 1       234     2345    | 7       345     8       | 2349    2359    6       | | 4578    6       234578  | 1       345     9       | 2347    2357    357     | |-------------------------+-------------------------+-------------------------| | 3       1       48      | 5       49      7       | 89      6       2       | | 9       247     6       | 234     8       234     | 5       37      1       | | 78      5       278     | 239     1       6       | 378     4       379     | *-----------------------------------------------------------------------------*`

yielding chain type 1:
conjugated als (59+4)
R1c3 (459)
R1c4(49)
R1c6(459)

removes 4 from
r1c2.

and the puzzle solves as singles.

This is from your posting on how Yielding Chains work.

StrmCkr wrote:Type One: Yielding Chain.

Is a Conjugated ALS that forms in a row /box /column that has a singular value common to all unknown cell in that space.

I guess you didn't notice that [r1c7]={37} doesn't contain a <4>, and thus [r1] doesn't qualify as a Type 1 Yielding Chain for (59+4).

However, all of the unknown cells do contain a <3>, and thus [r1] qualifies as a Type 1 Yielding Chain for (59+3). This then leads us to conclude that [r1c2]<>3 ... which is wrong!
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

This one is pretty good. There are all kinds of patterns here!

Code: Select all
`. 1 9|. . .|7 5 .. . 7|. . .|1 . .4 . .|. . .|. . 9-----+-----+-----. . .|6 . 7|. . .. . 2|9 . 3|6 . .5 . .|. . .|. . 3-----+-----+-----. 7 .|. . .|. 1 .. . 1|. 6 .|5 . .. . 6|3 2 1|4 . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

This one is a lot harder, according to SE, and somewhat harder according to SQ.

Code: Select all
`. . 1|6 . 8|9 . .  9 6 .|. . .|. 7 1. 2 .|. . .|. 8 .-----+-----+-----. 9 .|4 . 6|. 1 .3 . .|. . .|. . 9. . 5|. . .|2 . .-----+-----+-----. . 9|2 . 5|8 . .. . 6|1 . 4|5 . .. . .|. 6 .|. . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

I see a finned swordfish and a finned jellyfish, as well as lots of small-fry.

Code: Select all
`9 . .|. 1 8|. . 7. . 5|9 . 2|. . .. 6 .|. . .|. . .-----+-----+-----. 9 .|. 5 .|. 2 35 . .|2 . 9|. . 16 1 .|. 8 .|. 4 .-----+-----+-----. . .|. . .|. 1 .. . .|8 . 6|3 . .8 . .|1 9 .|. . 5`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

Not too bad, although SE rates it 7.1

Code: Select all
`. . 8|. . .|5 . .. 3 .|8 . 5|. 6 .4 . .|. 9 .|. . 7-----+-----+-----9 . .|6 . 1|. . 88 7 .|. . .|. 5 16 . .|. . .|. . 9-----+-----+-----. . .|5 . 2|. . .. 1 .|. 4 .|. 8 .. . 4|3 . 8|1 . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

This one is convoluted, twisted, busy...some of those.

Code: Select all
`. 1 9 | . . . | 7 5 .. . 7 | . . . | 1 . .4 . . | . . . | . . 9---------------------. . . | 6 . 7 | . . .. . 2 | 9 . 3 | 6 . .5 . . | . . . | . . 3---------------------. 7 . | . . . | . 1 .. . 1 | . 6 . | 5 . .. . 6 | 3 2 1 | 4 . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

This one is quite knotty. SE is 7.9, tied for highest in pattern
puzzles I have tested to date. SQ thinks much of it, too.

Code: Select all
`. . 1|6 . 8|9 . .9 6 .|. . .|. 7 1. 2 .|. . .|. 8 .-----+-----+-----. 9 .|4 . 6|. 1 .3 . .|. . .|. . 9. . 5|. . .|2 . .-----+-----+-----. . 9|2 . 5|8 . .. . 6|1 . 4|5 . .. . .|. 6 .|. . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

hey thanks for pointing an oversight in wording Daj

This is from your posting on how Yielding Chains work.

StrmCkr wrote:
Type One: Yielding Chain.

Is a Conjugated ALS that forms in a row /box /column that has a singular value common to all unknown cell in that space.

I guess you didn't notice that [r1c7]={37} doesn't contain a <4>, and thus [r1] doesn't qualify as a Type 1 Yielding Chain for (59+4).

However, all of the unknown cells do contain a <3>, and thus [r1] qualifies
as a Type 1 Yielding Chain for (59+3). This then leads us to conclude that [r1c2]<>3 ... which is wrong!

i should have been more specific on where a type 1 applies.

it should have read something more along the lines of this

....
A type one yielding chain also has all other unknown cells with 3+ candidates, where all cells have one common number containted in all of them.
...

type 1a.
which covered interactions of singluar bivavled cells in conjuction with the conjugated als.

which is what i did there and my mistake labeled it type 1 missing the "a" part.

proof of the move:

is done using coloring on cells where candidate will be removed when said number is found in one of the three cells.

I color in all cells containg the 4/7.
then execute the effect

when r1c347 = 3

where r1c2=4 &r 1c7=7

then the following grid is created.
Code: Select all
`  *-----------------------------------------------------------* | 6     4     359   | 3(9)    2     35@    | 7     1     8     | | 57    8     3579  | 6     4     1     | 239   2359  359   | | 2     3     1     | 8     7     35@    | 6     359   4     | |-------------------+-------------------+-------------------| | 57    9     2357  | 24-3   6     24-35  | 1     8     35    | | 1     23    235   | 7     35@    8     | 4     2359  6     | | 4     6     2358  | 1     35@    9     | 23    7     35    | |-------------------+-------------------+-------------------| | 3     1     4     | 5     9     7     | 89    6     2     | | 9     7     6     | 24-3   8     24-3   | 5     (3)!     1     | | 8     5     28    | 239   1     6     | 389   4     7     | *-----------------------------------------------------------*`

r4c47 & r8c47 form a deadly rectangle based on the positions of paired 35's and a expresed single three in r8c8

next i did another possible candidate.

when r1c3 = 7 (just to verify)

where r1c2=4 &r 1c7=3
Code: Select all
` didn't have to execute this one too far to find a visible error.(2 5's same block & 2's ) *--------------------------------------------------------------------* | 6      4      7      | 9      2      5!      | 3      1      8      | | 5      8      9      | 6      4    1      | 2!     2!     7      | | 2      3      1      | 8      7     5!      | 6      5    4      | |----------------------+----------------------+----------------------| `

then i did the thrid and final candidate

when r1c347 = 4

where r1c2=3/7 & r 1c7=3/7

no deadly patterns are left, all chains are compeleted as singles. (puzzle completed it's self as singles.)

the above events told me that the conjugated pairings 59+4 is the correct pair therefor -4 from r1c2

p.s
sorry for the clutter.

&
i do like the puzzles wapati keep um comming.

thanks for the fun and chance to see if these work or not.

strmckr
Some do, some teach, the rest look it up.

StrmCkr

Posts: 1170
Joined: 05 September 2006

rep'nA wrote:Edit: By the way, great puzzle wapati. I tend to look forward to working your puzzles each morning. Please keep them coming.
StrmCkr wrote:i do like the puzzles wapati keep um comming.

Thank you gentlemen! I appreciate the interest and will keep posting.

This one is pretty good, has some big-fins in it! Maltese falcon?

Code: Select all
`6 . . | . . . | . . 49 8 . | . 1 . | . 5 6. . 5 | 6 . 9 | 8 . .---------------------. . . | . . . | . . .2 1 . | . 5 . | . 4 78 . . | 1 . 4 | . . 9---------------------. 7 . | . . . | . 3 .. . . | 3 2 8 | . . .. . 8 | 7 6 1 | 4 . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

I found this one pretty tough.

Code: Select all
`. . 1 | 6 . 9 | 2 . .. 9 5 | 2 8 1 | 7 6 .. . . | . 4 . | . . .---------------------1 . . | . . . | . . 2. . 3 | 9 . 5 | 6 . .4 5 . | . . . | . 3 9---------------------. . . | . . . | . . .. 2 . | . 9 . | . 1 .. . 6 | . 2 . | 9 . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006